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Simplifying -7 = y2 + 8y + 5 Reorder the terms: -7 = 5 + 8y + y2 Solving -7 = 5 + 8y + y2 Solving for variable 'y'. Combine like terms: -7 + -5 = -12 -12 + -8y + -1y2 = 5 + 8y + y2 + -5 + -8y + -1y2 Reorder the terms: -12 + -8y + -1y2 = 5 + -5 + 8y + -8y + y2 + -1y2 Combine like terms: 5 + -5 = 0 -12 + -8y + -1y2 = 0 + 8y + -8y + y2 + -1y2 -12 + -8y + -1y2 = 8y + -8y + y2 + -1y2 Combine like terms: 8y + -8y = 0 -12 + -8y + -1y2 = 0 + y2 + -1y2 -12 + -8y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -12 + -8y + -1y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 8y + y2) = 0 Factor a trinomial. -1((6 + y)(2 + y)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve: Simplifying 6 + y = 0 Solving 6 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + y = 0 + -6 y = 0 + -6 Combine like terms: 0 + -6 = -6 y = -6 Simplifying y = -6Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2Solution
y = {-6, -2}
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